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ORIGINAL PAPER
Experiments on acoustic measurement of fractured rocksand application of acoustic logging data to evaluation of fractures
Bao-Zhi Pan1 • Ming-Xin Yuan1 • Chun-Hui Fang1 • Wen-Bin Liu1 •
Yu-Hang Guo1 • Li-Hua Zhang1
Received: 6 September 2016 / Published online: 21 July 2017
� The Author(s) 2017. This article is an open access publication
Abstract Fractures in oil and gas reservoirs have been the
topic of many studies and have attracted reservoir research
all over the world. Because of the complexities of the
fractures, it is difficult to use fractured reservoir core
samples to investigate true underground conditions. Due to
the diversity of the fracture parameters, the simulation and
evaluation of fractured rock in the laboratory setting is also
difficult. Previous researchers have typically used a single
material, such as resin, to simulate fractures. There has
been a great deal of simplifying of the materials and con-
ditions, which has led to disappointing results in applica-
tion. In the present study, sandstone core samples were
selected and sectioned to simulate fractures, and the
changes of the compressional and shear waves were mea-
sured with the gradual increasing of the fracture width. The
effects of the simulated fracture width on the acoustic wave
velocity and amplitude were analyzed. Two variables were
defined: H represents the amplitude attenuation ratio of the
compressional and shear wave, and x represents the transit
time difference value of the shear wave and compressional
wave divided by the transit time of the compressional
wave. The effect of fracture width on these two physical
quantities was then analyzed. Finally, the methods of
quantitative evaluation for fracture width with H and
x were obtained. The experimental results showed that the
rock fractures linearly reduced the velocity of the shear and
compressional waves. The effect of twin fractures on the
compressional velocity was almost equal to that of a single
fracture which had the same fracture width as the sum of
the twin fractures. At the same time, the existence of
fractures led to acoustic wave amplitude attenuations, and
the compressional wave attenuation was two times greater
than that of the shear wave. In this paper, a method was
proposed to calculate the fracture width with x and H, then
this was applied to the array acoustic imaging logging data.
The application examples showed that the calculated
fracture width could be compared with fractures on the
electric imaging logs. These rules were applied in the well
logs to effectively evaluate the fractures, under the case of
no image logs, which had significance to prospecting and
development of oil and gas in fractured reservoirs.
Keywords Fractured rock � Acoustic wave velocity �Acoustic wave amplitude � Experimental measurement �Fracture width
1 Introduction
Rock fractures are important oil storages and transport
channels. The physical properties of fractures, along with
the fractures’ development degree, are vital indices for
evaluating reservoirs. Therefore, fractured rock’s acoustic
and electrical parameters have become a focus for geo-
physicists and reservoir engineers. Many types of methods
have been used to evaluate fractures in seismic exploration
(Li 1997; Zhao et al. 2014; Kong et al. 2012). Among
these, the compressional wave anisotropy (Liu et al. 2012;
Ass’ad et al. 1992) and shear wave splitting (Baird et al.
2015; de Figueiredo et al. 2013; Gueguen and Sarout 2012)
are the most widely used methods at the present time to
evaluate fractures. The anisotropy and fracture parameters
& Li-Hua Zhang
1 Faculty of Geo-exploration Science and Technology, Jilin
University, Changchun 130012, Jilin, China
Edited by Jie Hao
123
Pet. Sci. (2017) 14:520–528
DOI 10.1007/s12182-017-0173-2
were obtained by seismic prospecting. However, the rela-
tionships between anisotropy and fractures are complex
and required further technical development. The qualitative
identification of fractures through conventional logs also
had certain developments (Sun et al. 2014; Deng et al.
2009; Wang 2013). However, using conventional logs
affected by many factors, as well as the limitations in
vertical resolution, has led to difficulties in obtaining
accurate identification of fractures. With the development
of computer technology, along with advancements in well
logging technology, imaging logs, like Formation
MicroScanner Image (FMI), had now become an accurate
basis for fracture identification (Qiao et al. 2005). How-
ever, because of high costs and the large amount of data, it
was difficult to use the imaging logs on an entire well and
in all wells (Aldenize et al. 2015). In addition, laboratory
fracture simulation experiments have been widely per-
formed. Due to fractures, the collected core samples from
boreholes broke easily, so that people cannot assess the
actual situation underground, thus it is difficult to measure
the fracture width of cores in the laboratory. Therefore, in
the laboratory, the simulation method was used for the
measurement of fractures in ultrasonic experiments (Far-
anak 2012). The physical simulation typically used a single
material to simulate the rock, constructing through artificial
means the pores and fractures to perform the measurement
of the acoustic wave velocity, quality factor and other
physical quantities with different fracture parameters (He
et al. 2001; Li et al. 2016; Amalokwu et al. 2014; Wang
et al. 2013). However, the single material simulation
experiment had neglected the complexity of the mineral
and pore distribution of the rock, so that the method was
still faced with many problems in actual application. In
addition, due to the fact that the acoustic wave attenuation
was much more complicated than the change of the
acoustic wave velocity, it was difficult to explain the
principles of the acoustic wave attenuation using the
physical model (Morris et al. 1964; Jose et al. 2013), thus
most of the methods of acoustic wave amplitude were
derived by means of numerical simulation, but the
boundary conditions were too simple to match many
problems in actual applications (Shi et al. 2004; Chen et al.
2012; Wang et al. 2015; Shragge et al. 2015).
It had been determined that the compressional and shear
wave velocities will change when a large number of rock
fractures exist (Quirein et al. 2015; Carcione et al. 2013).
Fractures led the velocities to become abnormal. The
relationship between the fracture width and the acoustic
parameters obtained in the laboratory was the key to esti-
mating fracture width. It has been found to be more
accurate to obtain the compressional and shear wave
velocities, as well as the acoustic wave amplitude, from the
dipole shear wave logging (DSI) and array acoustic logging
data (Xu et al. 2014; Chen and Tang 2012). Using the
inversion of DSI and array acoustic logging data to eval-
uate the fracture width, the application of this method for
the identification of fractures had very broad prospects and
feasibility (Wang et al. 2012).
This study was different from the physical experiments
of simulating fractures with a single material (Wei and Di
2007; Cao et al. 2004). Actual core samples were used to
simulate the fractured rocks. An ultrasonic experiment was
used to examine the acoustic parameters of the fractured
rocks. The effects of the pores of the rock itself on the
acoustic waves were eliminated. This point was found to be
more accurate than ignoring the rock porosity. The influ-
ences of different fracture width on the acoustic wave
velocity and amplitude were studied. Two variables were
defined: H represents the amplitude attenuation ratio of the
compressional and shear wave, and x represents the transit
time difference of shear wave and compressional wave
divided by the transit time of the compressional wave.
Transit time is the slowness of the acoustic wave. The
effects of fracture width on the two physical quantities,
H and x, were analyzed. The method of quantitative eval-
uation of fractures was achieved by using H and x. This
theory provided a new method for the quantitative calcu-
lations of fracture width, as well as the evaluation of
fractures in laboratory settings. This method has been
applied to actual well logging data and has obtained good
results. It also provided a basis for fractured reservoir
evaluation, which can be of assistance in the exploration
and development of oil fields in the future.
2 Experimental devices and measurementmethods
2.1 Preparation of samples and fractures
In this study, sandstone samples were cut across to simulate
fractured rocks. Table 1 displayed the parameters of the
core samples. The No. 1 and No. 2 samples were cut to
simulate fractured rocks.
Due to the evaporation of moisture, it was difficult to
maintain a unified state during the measurement of the
acoustic wave velocity in a fully saturated condition. The
Table 1 Parameters of the core samples
Length,
mm
Diameter,
mm
Mass, g Porosity,
%
1 47.27 24.98 48.59 18.9
2 48.98 24.9 54.35 12.5
3 38.96 24.92 48.19 18.9
Pet. Sci. (2017) 14:520–528 521
123
cores were kept dry during the measurement process, in
order to facilitate the comparison of the velocity change.
PET film was used to simulate the width of the fracture.
The PET film was formed into an annulus, with an outer
diameter of 24 mm, inner diameter of 20 mm and thickness
of 0.06 mm. The number of the PET film annuli was used
to control the width of fracture.
2.2 Method of measurement
The instrument used to conduct the experiment was an HF-
F Intelligent Ultrasonic Tester (Fig. 1a). A KDQS-II Full
Diameter Acoustic Analyzer (Fig. 1b) was the core holder
and used to measure the acoustic wave. The pass band-
width of the instrument was set at 0.1 to 1000 kHz. The
instrument launched the electrical signal, and the trans-
mitter probe transformed the signal into vibration. Then the
receiver probe converted the vibration into electrical volt-
age. The unit of amplitude was V, representing voltage.
The compressional and shear wave voltage transmitted by
the instrument was 250 V. Triggered by the computer, the
recording time length was 812.5 ls, the sampling interval
was 0.0625 ls, and the waveform length of each record
was 13,000 points. The acoustic wavelength launched by
the acoustic instruments was much less than the fracture
width. The measurements were taken at normal tempera-
ture and pressure. Wave propagation was along the vertical
axis of the rock. During the measurements, a good coupling
between the transducer and the rock was always main-
tained, and the transmitting and receiving transducer were
located at the ends of the center axis. There was a single
horizontal fracture in rock sample No. 1, and two parallel
horizontal fractures in the rock sample No. 2 (Fig. 1c).
3 Repetitive experiment
The effects of accidental factors on acoustic propagation
can be eliminated through repeated experiments. Due to the
influence of different fracture width on the acoustic wave
velocity and amplitude, the fracture width (Wf) was made
at 0.18 mm with layers of PET film. The experiment was
repeated three times, measuring the compressional and
shear wave velocity (Vp, Vs) and amplitude (Ap, As) of the
No. 1 samples. The test results are shown in Table 2.
As can be seen from Table 2, the four parameters of
sample No.1 from three repeated measurements were very
similar and the relative standard deviation values were
relatively small. It was safe to conclude that the results
were stable and repeatable, which provided a reliable basis
for our subsequent data analysis.
4 Results and analysis
4.1 Velocity measurement and analysis of core
with a single fracture
The influence of fracture width on the acoustic wave
velocity was investigated. Figure 2 showed rock’s varia-
tion of compressional wave velocity with the widths of the
fracture of sample No. 1. The widths of the fractures were
from 0 to 7 units, 0, 0.06, 0.12, 0.18, 0.24, 0.30, 0.36 and
0.42 mm. The thickness of each unit represented a layer of
PET film.
When the fracture width was less than 0.42 mm, the
variation of the Vp along with the fracture widths was
obtained by fitting the measured data as follows.
Vp ¼ �1509:8�Wf þ 2797:6 ð1Þ
The variation of the Vs along with the fracture was as
follows.
Vs ¼ �399:48�Wf þ 1597:3 ð2Þ
Fig. 1 Experimental instruments and rock samples. HF-F Intelligent
Ultrasonic Tester (a), KDQS-II Full Diameter Acoustic Analyzer (b),two rock samples (c)
Table 2 Acoustic wave measurement of sample No. 1’s repeatability
of the Wf = 0.18 mm
Vp, m/s Ap, V Vs, m/s As, V
1 2525.8 1010.3 1525.4 846.9
2 2577.2 1007.5 1513.8 868.5
3 2581.8 985.7 1526.7 795.7
RSD (%) 2.79 3.09 1.07 1.1
RSD (%) = 100 9 standard deviation/the arithmetic mean of the
calculated results
522 Pet. Sci. (2017) 14:520–528
123
The above results showed that there were obvious
relationships between the acoustic wave velocity and the
development degrees of fractures in the rock.
The existence of fractures led to velocity decrease for
both the compressional and shear waves. With the increa-
ses of the fracture width, the velocity continued to decrease
and displayed a linear relationship when the fracture width
was less than 0.42 mm. From the slope of the fitting line, it
could be seen that the changes of shear wave velocity were
smaller than those of the compressional wave. Thus, the
existence of fractures and fracture width were the influence
factors of the compressional and shear wave velocity.
The measured values obtained in the acoustic logging
were the acoustic transit time. Therefore, the relationships
between the velocity of the acoustic wave and the width of
the fractures could be converted into the relationships
between the acoustic transit time and the fracture width. In
this study, in order to eliminate the influence of the rock’s
porosity on the acoustic transit time and make the changes
of the compressional and shear wave transit time only
related to the fracture width, x was defined as follows:
x ¼ DTs � DTp� ��
DTp ð3Þ
where DTs is the transit time of the shear wave, s/m, which
was 1/Vs; and DTp is the transit time of the compressional
wave, s/m, which was 1/Vp.
The relationship between the fracture width and x of
sample No. 1 is illustrated in Fig. 3.
In accordance with the data shown in Fig. 3, the formula
for calculating the fracture width, Wf, mm, was determined
as follows:
Wf ¼ �1:6393xþ 1:253 ð4Þ
4.2 Velocity analysis of rocks with multiple fractures
In actual reservoirs, there are multiple fractures, rather than
a single fracture. The impact of two parallel fractures on
acoustic wave velocity was measured, and the acoustic
wave velocities with the same width as a single fracture
were compared. In dry conditions, between one and three
PET films were placed in the two fractures of core sample
No. 2, in order to simulate two parallel fractures with
widths of 0.06, 0.12 and 0.18 mm. The relationships
between the compressional wave velocity and the two
parallel fracture widths were examined, and a comparison
with the single fracture sample which had the same fracture
width was performed. The results are shown in Fig. 4.
Figure 4 shows that multiple fractures caused the com-
pressionalwave velocity to be approximately linearly reduced.
Furthermore, when the fracture width was less than 0.36 mm,
two parallel fractures had almost the same influence on the
compressional wave velocity as the single fracture.
4.3 Analysis of the relationship
between the amplitude attenuation and fracture
width
The fracture widths of core sample No. 1 were 0, 0.06,
0.12, 0.18, 0.24, 0.30 and 0.36 mm. In order to compare the
0
500
1000
1500
2000
2500
3000
0 0.1 0.2 0.3 0.4 0.5
Vp
Vs
V, m
*s- 1
Wf , mm
Vp=-1509.8Wf+2797.6
Vs=-399.49Wf+1597.3
Fig. 2 Relationship between fracture widths and acoustic wave
velocity of No. 1 rock. The filled circles and squares, respectively,
represented the compressional and shear wave velocity of the core
with the fracture. The fracture widths Wf in the core were 0; 0.06;
0.12; 0.18; 0.24; 0.3; 0.36 and 0.42 mm
0
0.1
0.2
0.3
0.4
0.5
0 0.2 0.4 0.6 0.8
Wf ,
mm
x
Wf =-1.6393x+1.253
Fig. 3 Relationship between the fracture width and x
2000
2200
2400
2600
2800
3000
0 0.1 0.2 0.3 0.4
Single fracture
Parallel fracture
V p, m
*s- 1
Wf , mm
Fig. 4 Velocity contrasts of the single and two parallel fractures. The
filled circles and squares, respectively, represent the single and twin
fractures compressional wave velocities of the core with the fracture.
The single fracture widths in the core were Wf = 0; 0.06; 0.12; 0.18;
0.24; 0.3 and 0.36 mm. The two fracture widths in the core were
Wf = 0; 0.12; 0.24; 0.30 and 0.36 mm
Pet. Sci. (2017) 14:520–528 523
123
attenuation of the acoustic wave amplitudes, the amplitude
of the compressional and shear waves was corrected to the
same gain value using Eq. (5):
A2 ¼ A1 � e0:1085� y2�y1ð Þ ð5Þ
where y1 was the gain before the correction; y2 was the goal
gain; A1 was the amplitude before the correction, and A2
was the amplitude after the correction. The amplitude after
the correction was shown in Fig. 5.
The variation of the compressional wave amplitude, Ap,
with the changes of the fracture width was obtained by
fitting the measured data as follows:
Ap ¼ 2:0663� e�3:5Wf ð6Þ
The variation of shear wave amplitude, As, with the
changes of the fracture widths was obtained by fitting the
measured data as follows:
As ¼ 1:1407� e�1:288Wf ð7Þ
With the increases of the fracture width, the amplitudes
of the shear and compressional wave were exponentially
reduced. Apmax was the maximum amplitude of the com-
pressional wave without fractures; and Asmax was the
maximum amplitude of the shear wave without fractures.
Amax - A was defined as the difference between acoustic
wave amplitude without fracture and that with fractures.
The relationship between Amax - A and the fracture width
is shown in Fig. 6.
FromFig. 6, it can be seen that, when therewere fractures,
the attenuation of the compressional wave was faster than
that of the shear wave. The difference between Apmax - Ap
and Asmax - As increased gradually with the increase of
fracture width. The ratio between the attenuation of com-
pressional wave and the attenuation of shear wave was
defined as H, in order to study the effect of fracture width.
H ¼ ðApmax � ApÞ�ðAsmax � AsÞ ð8Þ
Figure 7 illustrates the relationship between H and the
fracture width.
When the fracture width was less than 0.36 mm, the
relationship between H and fracture width, Wf, was
obtained by fitting the measured data as follows:
H ¼ �12:49þ 14:43e�Wf þ 22:59Wf � e�Wf ð9Þ
Equation (9) shows that when the fracture width was
less than 0.36 mm, the greater the fracture width was, the
greater the H was, and the H tended to be stable. The
relationship was summarized, and the empirical value of
H was used to evaluate the fracture width. The experiment
showed that when H was greater than 2, there was a
fracture.
5 Application examples of identifying fracturesbased on acoustic logging data
In order to verify the accuracy of Eq. (4), the DSI data of a
well were calculated to evaluate the fractures. The depths
from 2780 m to 2810 m and from 3008 m to 3060 m were
0
0.5
1.0
1.5
2.0
2.5
0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Ap
As
A, V
Wf , mm
Fig. 5 Relationship between the fractures width and the amplitude of
the acoustic wave. The filled circle and square represent the
compressional and shear wave amplitudes of the core with the
fracture. The fracture widths in the core were = 0; 0.06; 0.12; 0.18;
0.24; 0.3 and 0.36 mm
0
0.3
0.6
0.9
1.2
1.5
1.8
0 0.1 0.2 0.3 0.4
Apmax-Ap
Asmax-As
A max-A
, V
Wf , mm
Fig. 6 Relationship between fracture width and acoustic wave
amplitude attenuation. The filled squares and circles represent the
Apmax - Ap and Asmax - As. The fracture widths in the core were
Wf = 0; 0.06; 0.12; 0.18; 0.24; 0.3 and 0.36 mm
1.8
2.2
2.4
2.6
2.8
3.2
3.4
0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
H
3.0
2.0
Wf , mm
H =-12.49+14.43e-Wf +22.59Wf ×e-Wf
Fig. 7 Relationship between H and the fracture width
524 Pet. Sci. (2017) 14:520–528
123
two sections in which fractures were developed (Fig. 8).
Since electrical imaging logging was a good method for
identifying fractures, imaging log data were used to vali-
date the results.
In Fig. 8, the first track represents depth. The second
track is the transit time of the compressional wave and
shear wave, which were extracted from the DSI log data.
The third track is the width of fractures by Eq. (4),
obtained by calculating x according to the transit time. The
fourth is the electrical imaging of FMI. The following four
tracks show the fracture characteristics calculated from
FMI, which were used to compare the calculation results of
the fracture width.
The fracture-developed sections were located at 2784 to
2799 m (I), 3010 to 3015 m (II), 3033 to 3037 m (III) and
3051 to 3054 m (IV). Figure 8 illustrated that the
Depth
Depth
1:200
2780.0
DTp (µs/ft)
IMAGE.DYNA
Wf
DTs (µs/ft)
0.0 0.0
0.0 0.00.0 0.0FVTL FVDC FVAH FVPA20.0 10.0 0.0 10.0 0.0 0.02
0
250
2560.00.0
200.0
200.0
0.15
0.15
0.15
2790.0
2800.0
3010.0
3020.0
3030.0
3040.0
3050.0
3060.0
(m)
Acoustic transit time Fracture width Dynamic image Fracture length Fracture density Average hydrodynamic width Fracture porosity
(I)
(II)
(III)
(IV)
Fig. 8 Sections logging data at 2780 to 2800 m and 3010 to 3060 m in well A
Pet. Sci. (2017) 14:520–528 525
123
calculated results through Eqs. (3) and (4) were coincident
to the fractures of FMI.
Figure 9 illustrates the comparison of the H and FMI
data of well B. The second track is the acoustic wave
amplitude, and the third track is the acoustic wave atten-
uation. The fourth track represents H. The sixth is the static
image and the fracture tracing. The seventh shows the
tadpole plot of the fracture dip according to the imaging
log, GR, and caliper curve. The last track is the dynamic
image.
The pink area in Fig. 9 is the calculated H. It can be seen
that the ratio was greater than 2 when the fracture devel-
oped. The results of the fracture evaluations were coinci-
dent to the fractures of FMI, which were in accordance
with H. Due to the fact that the acoustic wave amplitude
was sensitive to the response of the fracture, in the section
of the fracture developed, the amplitude was attenuated.
Therefore, when using the acoustic wave velocity to cal-
culate the fracture, the resolution of the acoustic wave
amplitude was higher. The exact calculation of fracture
width from H remains to be studied.
6 Conclusions
1. The existence of fractures led to decrease of the
acoustic wave velocity. The shear and compressional
wave velocities were found to linearly decrease with
the increases of the fracture width. The decrease of the
compressional wave velocity was faster than the shear
wave. The velocity of the acoustic wave was converted
to the transit time. The ratios of the transit time of
compressional wave and shear wave (x) were affected
by fracture width, when the fracture width was less
than 0.42 mm. With the increase of fracture width,
x was becoming smaller and smaller. Fracture width
can be calculated through the relationship between
x and the fracture width.
2. The existence of fractures led to a decrease of the
amplitudes of the compressional and shear wave. With
the increase of the fracture width, the amplitudes of the
compressional and shear wave decreased exponen-
tially. The amplitude attenuation ratio (H) was defined,
when there was a fracture, the H value was greater than
Depth Acoustic amplitude Acoustic attenuation H Depth Static image Fracture diptadpole plot Dynamic image
Depth Depth
0.0
25702572
25742576
25702572
25742576
26162618
26202622
26162618
26202622
30.0 0.0 30.0
2 5
2 5
2 50.0
Ap
As
[DP1]
[DP1]
Apmax-Ap
H
Asmax-As
[DP1] [DP0]
Fractureexpanded image
0.0 100.0
API[DP0]Natural gamma
0.0 200
[DP1]
[DP1]
[DP0]
[DP0]
Static image
Fracture dip tadpole plot
2400
0.0 90
cm[DP0]
Calliper1
0.0 26
cm[DP0]
Calliper2
0.0 26
cm[DP0]
Calliper3
0.0 261200
3600
[DP0]
Fractureexpanded image
0.0 100.0
[DP0]
Dynamic image
24001200
3600
30.0 0.0 30.0(m) (m)
Fig. 9 Comparison of the amplitudes and imaging results at 2570 to 2576 m and 2616 to 2623 m
526 Pet. Sci. (2017) 14:520–528
123
2. When the fracture width was less than 0.36 mm, the
empirical value of H was gradually increased. Accord-
ing to this experience, the position of fractures in the
reservoir can be located.
3. By measuring the effects of both the single and two
parallel fractures on the compressional wave velocity,
it was determined that when the width of the parallel
fractures was equal to that of a single fracture, they had
the same effect on the compressional wave velocity.
This result was only applicable to the compressional
wave, because the compressional wave velocity was
less affected by the number of fractures.
4. Through experimental measurements, the method for
evaluating fractures in the borehole by using x and
H also was achieved. This study used wells A and B as
application examples. The calculation results were
compared with FMI data, with good agreement. The
results verified that the rock acoustic parameters were
affected by fractures in the borehole and provided a
new method for the quantitative evaluation of frac-
tures. In actual production, because of the influence of
the fracture dip and fracture filler, this conclusion may
exhibit a certain deviation, thus it will be studied by
the authors in the future.
5. The next step will be to study the fracture of carbonate
reservoirs and shale reservoirs.
Acknowledgements This work was supported in part by the National
Natural Science Foundation of China (Grant No. 41174096) and was
supported by the Graduate Innovation Fund of Jilin University (Pro-
ject No. 2016103).
Open Access This article is distributed under the terms of the
Creative Commons Attribution 4.0 International License (http://crea
tivecommons.org/licenses/by/4.0/), which permits unrestricted use,
distribution, and reproduction in any medium, provided you give
appropriate credit to the original author(s) and the source, provide a
link to the Creative Commons license, and indicate if changes were
made.
References
Aldenize X, Carlos EG, Andre A. Fracture analysis in borehole
acoustic imaging using mathematical morphology. J Geophys
Eng. 2015;3(12):492–501. doi:10.1088/1742-2132/12/3/492.
Amalokwu K, Best AI, Sothcott J, et al. Water saturation effects on
elastic wave attenuation in porous rocks with aligned fractures.
Geophys J Int. 2014;197:943–7. doi:10.1093/gji/ggu076.
Ass’ad JM, Tatham RH, McDonald JA. A physical model study of
microcrack-induced anisotropy. Geophysics. 1992;57(12):1562–
70. doi:10.1190/1.1443224.
Baird AF, Kendall JM, Sparks RSJ, et al. Transtensional deformation
of Montserrat revealed by shear wave splitting. Earth Planet Sci
Lett. 2015;425:179–86. doi:10.1016/j.epsl.2015.06.006.
Cao J, He ZH, Huang DJ, et al. Physical modeling and ultrasonic
experiment of pore-crack in reservoirs. Prog Geophys.
2004;19(2):386–91 (in Chinese).Carcione JM, Gurevich B, Santos JE. Angular and frequency-
dependent wave velocity and attenuation in fractured porous
media. Pure Appl Geophys. 2013;11(170):1673–83. doi:10.1007/
s00024-012-0636-8.
Chen Q, Liu XJ, Liang LX, et al. Numerical simulation of the
fractured model acoustic attenuation coefficient. Geophysics.
2012;55(6):2044–52. doi:10.6038/j.issn.0001-5733.2012.06.026
(in Chinese).Chen XL, Tang XM. Numerical study on the characteristics of
acoustic logging response in the fluid-filled borehole embedded
in crack-porous medium. Chin J Geophys. 2012;55(6):2129–40.
doi:10.6038/j.issn.0001-5733.2012.06.035 (in Chinese).de Figueiredo JJS, Schleicher J, Stewart RR, et al. Shear wave
anisotropy from aligned inclusions: ultrasonic frequency depen-
dence of velocity and attenuation. Geophys J Int. 2013;193:
475–88. doi:10.1093/gji/ggs130.
Deng M, Qu GY, Cai ZX. Fracture identification for carbonate
reservoir by conventional well logging. Geol J. 2009;33(1):75–8
(in Chinese).Faranak M. Anisotropy estimation for a simulated fracture medium
using traveltime inversion: a physical modeling study. In: 2012
SEG annual meeting; 2012.
Gueguen Y, Sarout J. Characteristics of anisotropy and dispersion in
cracked medium. Tectonophysics. 2012;503:165–72. doi:10.
1016/j.tecto.2010.09.021.
He ZH, Li YL, Zhang F, et al. Different effects of vertically oriented
fracture system on seismic velocities and wave amplitude.
Comput Tech Geophys Geochem Explor. 2001;23(1):01–5 (inChinese).
Jose CM, Gurevich B, Santos JE. Angular and frequency-dependent
wave velocity and attenuation in fractured porous media. Pure
Appl. Geophys. 2013;11(170):1673–1683. doi:10.1007/s00024-
012-0636-8.
Kong LY, Wang YB, Yang HZ. Fracture parameters analyses in
fracture-induced HTI double-porosity medium. Geophysics.
2012;55(1):189–96. doi:10.6038/j.issn.0001-5733.2012.01.018
(in Chinese).Li TY, Wang RH, Wang ZZ. Experimental study on the effects of
fractures on elastic wave propagation in synthetic layered rocks.
Geophysics. 2016;81(4):441–51. doi:10.1190/geo2015-0661.1.
Li XY. Fractured reservoir delineation using multicomponent seismic
data. Geophys Prospect. 1997;45:39–64. doi:10.1046/j.1365-
2478.1997.3200262.x.
Liu ZF, Qu SL, Sun JG. Progress of seismic fracture characterization
technology. Geophys Prospect Pet. 2012;51(2):191–8 (inChinese).
Morris RL, Grine DR, Arkfeld TE. Using compressional and shear
acoustic amplitudes for the location of fractures. J Pet Technol.
1964;16(6):623–5.
Qiao DX, Li N, Wei ZL, et al. Calibrating fracture width using
Circumferential Borehole Image Logging data from model wells.
Pet Explor Dev. 2005;1:76–9 (in Chinese).Quirein J, Far M, Gu M, et al. Relationships between sonic
compressional and shear logs in unconventional formations. In:
SPWLA 56th annual logging symposium; 2015.
Shi G, He T, Wu YQ, et al. A study on the dual laterolog response to
fractures using the forward numerical modeling. Chin J
Geophys. 2004;47(2):359–63 (in Chinese).Shragge J, Blum TE, van Wijk K, et al. Full-wavefield modeling and
reverse time migration of laser ultrasound data: a feasibility
study. Geophysics. 2015;80(6):D553–63. doi:10.1190/geo2015-
0020.1.
Pet. Sci. (2017) 14:520–528 527
123
Sun W, Li YF, Fu JW. Review of fracture identification with well logs
and seismic data. Pet Geol Exp. 2014;29(3):1231–42 (inChinese).
Wang RH, Wang ZZ, Shan X, et al. Factors influencing pore-
pressure prediction in complex carbonates based on effective
medium theory. Pet Sci. 2013;10:494–9. doi:10.1007/s12182-
013-0300-7.
Wang RJ, Qiao WX, Ju XD. Numerical study of formation anisotropy
evaluation using cross dipole acoustic LWD. Chin J Geophys.
2012;55(11):3870–82. doi:10.6038/j.issn.0001-5733.2012.11.
035 (in Chinese).Wang RX. Summary of the convention logging to identify fractures.
Shandong Ind Technol. 2013;7:128–9 (in Chinese).
Wang ZZ, Wang RH, Li TY, et al. Pore-scale modeling of pore
structure effects on P-wave scattering attenuation in dry rocks.
PLoS ONE. 2015. doi:10.1371/journal.pone.0126941.
Wei JX, Di BR. Experimentally surveying influence of fractural
density on P-wave propagating characters. Oil Geophys
Prospect. 2007;42(5):554–9 (in Chinese).Xu S, Su YD, Chen XL, et al. Numerical study on the characteristics
of multipole acoustic logging while drilling in cracked porous
medium. Chin J Geophys. 2014;57(6):1992–2012. doi:10.6038/
cjg20140630 (in Chinese).Zhao WH, Sun DS, Li AW, et al. Experimental study on the effect of
fracture on seismic wave velocity. In: China earth sciences joint
annual conference; 2014. p. 2896–99 (in Chinese).
528 Pet. Sci. (2017) 14:520–528
123